 # 9.12 Diffraction grating • Order of diffraction

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9.12 Diffraction grating • Order of diffraction
• Relationship between d,  and  • Diffraction of white light © Manhattan Press (H.K.) Ltd.

Waves diffracted through slits
9.12 Diffraction grating (SB p. 104) Diffraction grating Diffracting grating – a glass or plastic consists of many fine parallel lines Waves diffracted through slits © Manhattan Press (H.K.) Ltd.

Order of diffraction 1. Zeroth order diffraction
9.12 Diffraction grating (SB p. 104) Order of diffraction 1. Zeroth order diffraction a set of plane P wavefronts moves forwards zero order diffraction (high intensity light detected) © Manhattan Press (H.K.) Ltd.

Order of diffraction 2. First order diffraction
9.12 Diffraction grating (SB p. 105) Order of diffraction 2. First order diffraction a set of plane Q wavefronts moves forwards first order diffraction © Manhattan Press (H.K.) Ltd.

Order of diffraction 3. Second order diffraction
9.12 Diffraction grating (SB p. 105) Order of diffraction 3. Second order diffraction a set of plane R wavefronts moves forwards Second order diffraction © Manhattan Press (H.K.) Ltd.

Relationship between d,  and 
9.12 Diffraction grating (SB p. 105) Relationship between d,  and  d sinn = n © Manhattan Press (H.K.) Ltd.

Relationship between d,  and 
9.12 Diffraction grating (SB p. 106) Relationship between d,  and  Measure n by spectrometer - wavelength of light  can be determined d sinn = n Slit separation d = (N - no. of lines per unit length) © Manhattan Press (H.K.) Ltd.

Diffraction of white light
9.12 Diffraction grating (SB p. 106) Diffraction of white light other orders of diffraction (colour spectra) zero order diffraction (white) Go to Example 18 Red – greater diffraction angle Violet – smaller diffraction angle © Manhattan Press (H.K.) Ltd.

Summary 9.1 Huygen’s principle
9.12 Diffraction grating (SB p. 110) Summary 9.1 Huygen’s principle 1. Huygens’ principle states that: (a) All the points of a wavefront behave as sources emitting secondary wavelets. (b) The new position of the wavefront is the surface which is tangential to all the wavelets. © Manhattan Press (H.K.) Ltd.

9.12 Diffraction grating (SB p. 110)
Summary 9.2 Reflection 2. Reflection occurs when a wave meets a straight barrier. 3. According to the law of reflection, the angle of reflection is equal to the angle of incidence. 4. The applications of reflection include radar, sonar and long distance propagation of radio waves. © Manhattan Press (H.K.) Ltd.

9.12 Diffraction grating (SB p. 110)
Summary 9.2 Reflection 5. (a) When a wave hits a fixed end, the reflected wave and the incident wave are out of phase. (b) When a wave hits a free end, the reflected wave and the incident wave are in phase. © Manhattan Press (H.K.) Ltd.

9.12 Diffraction grating (SB p. 110)
Summary 9.3 Refraction 6. Refraction occurs when a wave moves from one medium to another, resulting a change in wave speed. 7. By Snell’s law, where n is the refractive index. © Manhattan Press (H.K.) Ltd.

9.12 Diffraction grating (SB p. 110)
Summary 9.3 Refraction 8. When a water wave moves from a shallow region to a deep region, (a) its speed increases; (b) its wavelength increases; and (c) it is refracted away from the normal. © Manhattan Press (H.K.) Ltd.

Summary 9.4 Polarization of light waves
9.12 Diffraction grating (SB p. 110) Summary 9.4 Polarization of light waves 9. Polarization is the restriction of the vibrations in a wave so that the vibrations occur in a single plane. It only occurs in transverse waves. 10. A device that allows electric field of light to vibrate in only one directions and simultaneously absorbs all other electric fields vibrating in different directions is known as polarizer. © Manhattan Press (H.K.) Ltd.

Summary 9.4 Polarization of light waves
9.12 Diffraction grating (SB p. 110) Summary 9.4 Polarization of light waves 11. The intensity of light (I) emerging from an analyser Q is I = Io cos2θ where Io is the intensity of light incident on Q. 12. By rotating a polarizer to see whether there is an intensity change of light from maximum to minimum (no light), it is able to test if the light is plane polarized or not. © Manhattan Press (H.K.) Ltd.

Summary 9.4 Polarization of light waves
9.12 Diffraction grating (SB p. 110) Summary 9.4 Polarization of light waves 13. If a polarizer is used to select one specific direction of vibration of the wave, then the process is called polarization by selective absorption. 14. A piece of polaroid can be used to polarize light waves. © Manhattan Press (H.K.) Ltd.

Summary 9.4 Polarization of light waves
9.12 Diffraction grating (SB p. 110) Summary 9.4 Polarization of light waves 15. Brewster’s Law states that when the angle of incidence i at the reflecting surface satisfies the following equation: tan i = n (where n is the refractive index of the material) the polarization is complete. The angle i is also known as Brewster angle. © Manhattan Press (H.K.) Ltd.

Summary 9.4 Polarization of light waves
9.12 Diffraction grating (SB p. 110) Summary 9.4 Polarization of light waves 16. If light propagates through a gas (or liquid), the electrons in the gas can absorb and re-radiate part of the light. The absorption and re-radiation of light by the gas is called scattering. 17. The main applications of polarization of light include sunglasses and receiving radio wave signals. © Manhattan Press (H.K.) Ltd.

Summary 9.5 Superposition
9.12 Diffraction grating (SB p. 111) Summary 9.5 Superposition 18. The principle of superposition of waves states that when two waves pass any point in a medium at the same instant, the resultant displacement at the point is equal to the sum of the individual displacements due to each of the waves. © Manhattan Press (H.K.) Ltd.

9.12 Diffraction grating (SB p. 111)
Summary 9.6 Beats 19. The periodic variation in the loudness of a sound which is heard when two notes of almost the same frequency are played simultaneously is called beats. 20. The beat frequency is the difference between the frequencies of the two waves. © Manhattan Press (H.K.) Ltd.

9.12 Diffraction grating (SB p. 111)
Summary 9.7 Diffraction 21. Diffraction is the bending of waves around an obstacle or through a gap. 22. The wider the gap or the larger the obstacle (compared with the wavelength), the less the bending becomes. 23. Fraunhofer diffraction is the diffraction of light produced by a narrow slit when plane light waves are incident normally on the slit and light waves emerging from the slit are plane waves. © Manhattan Press (H.K.) Ltd.

9.12 Diffraction grating (SB p. 111)
Summary 9.7 Diffraction 24. In general, minima occurs when (θis small) where n = 1, 2, 3, ... 25. When the slit width decreases, the angle θincreases. This means that a broader central maximum is obtained but the intensity of all the bright fringes decreases. © Manhattan Press (H.K.) Ltd.

Summary 9.8 Interference of water waves
9.12 Diffraction grating (SB p. 111) Summary 9.8 Interference of water waves 26. Interference is the effect produced by the superposition of waves from two coherent sources passing through the same region. 27. (a) The condition for constructive interferences in terms of path difference: p.d. = nλ (b) The condition for destructive interferences in terms of path difference: p.d. = (n – )λ © Manhattan Press (H.K.) Ltd.

Summary 9.8 Interference of water waves
9.12 Diffraction grating (SB p. 111) Summary 9.8 Interference of water waves 28. (a) The line joining all the antinodes is known as an antinodal line. (b) The line joining all the nodes is known as a nodal line. 29. The resultant displacement of two waves: y = y0 sin(t + ) where y0 = 2a cos . 30. A phasor diagram can be used to find the displacement of any point in a wave. © Manhattan Press (H.K.) Ltd.

Summary 9.9 Optical path length
9.12 Diffraction grating (SB p. 111) Summary 9.9 Optical path length 31. When light travels through a medium of refractive index n, and the distance travelled is l, the optical path length is given by nl. 32. For the same time interval, the optical path length is the same in all media. © Manhattan Press (H.K.) Ltd.

Summary 9.10 Interference of light waves
9.12 Diffraction grating (SB p. 111) Summary 9.10 Interference of light waves 33. Young’s double slit experiment is used to demonstrate the interference of light waves. 34. When a monochromatic light of wavelength λ is incident on a double slit of slit separation a, the fringe separation x : (for bright fringe) where D is the distance of a screen from the double slit. © Manhattan Press (H.K.) Ltd.

Summary 9.10 Interference of light waves
9.12 Diffraction grating (SB p. 111) Summary 9.10 Interference of light waves 35. (a) Energy is re-distributed for the constructive and destructive interference. (b) Since I ∝ a2, the intensity of the bright fringes produced by a double-slit is four times that by a single-slit. © Manhattan Press (H.K.) Ltd.

Summary 9.11 Practical examples of interference
9.12 Diffraction grating (SB p. 112) Summary 9.11 Practical examples of interference 36. Applications of interference in thin films include the “blooming” of lenses to produce “non-reflective” lenses and the testing of surface flatness. 37. If monochromatic light is incident on a parallel-sided or wedge-sided thin film, dark and bright fringes will be observed. © Manhattan Press (H.K.) Ltd.

Summary 9.11 Practical examples of interference
9.12 Diffraction grating (SB p. 112) Summary 9.11 Practical examples of interference 38. For the wedge-sided thin film, at the touched end of the slides, despite the path difference of the two reflected rays is zero, there is a 180°phase change on the reflected ray from the glass block. Thus, a dark fringe is produced. © Manhattan Press (H.K.) Ltd.

Summary 9.11 Practical examples of interference
9.12 Diffraction grating (SB p. 112) Summary 9.11 Practical examples of interference 39. Because the oil film / soap film thickness varies, the path difference is different along the film surface, together with different viewing angles, producing an interesting colour pattern. 40. When a beam of monochromatic light is incident normally on a plano-convex lens, a series of dark and bright rings is observed. These rings are called Newton’s rings. © Manhattan Press (H.K.) Ltd.

Summary 9.12 Diffraction grating
9.12 Diffraction grating (SB p. 112) Summary 9.12 Diffraction grating 41. A diffraction grating consists of many fine parallel lines ruled closely on a piece of glass or plastic. 42. The transmitted light is channelled only in certain directions known as the orders of diffraction. © Manhattan Press (H.K.) Ltd.

Summary 9.12 Diffraction grating
9.12 Diffraction grating (SB p. 112) Summary 9.12 Diffraction grating 43. When plane waves of wavelength λ are incident normally on a diffraction grating of slit separation d, for the nth order diffraction, d sinθn = nλ where n = 0, 1, 2, 3, ... θ is the angle between the diffracted light and the normal. 44. When white light is used, the zeroth order diffraction is white. For the other orders of diffraction, white light is separated into colour spectrum. © Manhattan Press (H.K.) Ltd.

Concept Map 9.12 Diffraction grating (SB p. 113)

End © Manhattan Press (H.K.) Ltd.

9.12 Diffraction grating (SB p. 107)
Example 18 Q: Light from a source is incident normally on a diffraction grating which has lines per cm. If the light consists of two lines of wavelength 656 nm and 410 nm respectively, determine the angular separation between the two lines in the second order spectrum produced by the grating. Solution © Manhattan Press (H.K.) Ltd.

9.12 Diffraction grating (SB p. 107)
Example 18 Solution: Use the equation dsinn = n When n = 2, and  = 656 nm = 2 × (656 × 109)  2 = 31.65 For  = 410 nm, = 2 × (410 × 109)  2’ = 19.15  Angular separation = 31.65  19.15 = 12.5 Return to Text © Manhattan Press (H.K.) Ltd.